Image Denoising Methods for Tumor Discrimination in High-Resolution Computed Tomography

Pixel accuracy in images from high-resolution computed tomography (HRCT) is ultimately limited by reconstruction error and noise. While for visual analysis this may not be relevant, for computer-aided quantitative analysis in either densitometric, or shape studies aiming at accurate results, the impact of pixel uncertainty must be taken into consideration. In this work, we study several denoising methods: geometric mean filter, Wiener filtering, and wavelet denoising. The performance of each method was assessed through visual inspection, profile region intensity analysis, and global figures of merit, using images from brain and thoracic phantoms, as well as several real thoracic HRCT images

Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

[EN] In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials.Partial financial support for this work has been given by grant DPI2011-26635 from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of SpainLatorre, M.; Montáns, FJ. (2015). Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains. Computational Mechanics. 56(3):506-531. https://doi.org/10.1007/s00466-015-1184-8506531563Cristensen RM (2003) Theory of viscoelasticity. Elsevier, DoverShaw MT, MacKnight WJ (2005) Introduction to polymer viscoelasticity. Wiley-Blackwell, New YorkArgon AS (2013) The physics of deformation and fracture of polymers. Cambridge University Press, CambridgeSchapery RA, Sun CT (eds) (2000) Time dependent and nonlinear effects in polymers and composites. American Society for Testing and Materials (ASTM), West ConshohockenGennisson JL, Deffieux T, Macé E, Montaldo G, Fink M, Tanter M (2010) Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging. Ultrasound Med Biol 36(5):789–801Schapery RA (2000) Nonlinear viscoelastic solids. Int J Solids Struct 37(1):359–366Truesdell C, Noll W (2004) The non-linear field theories of mechanics. Springer, BerlinRivlin RS (1965) Nonlinear viscoelastic solids. SIAM Rev 7(3):323–340Fung YC (1993) A first course in continuum mechanics. Prentice-Hall, Upper Saddle RiverFung YC (1972) Stress–strain-history relations of soft tissues in simple elongation. Biomechanics 7:181–208Sauren AAHJ, Rousseau EPM (1983) A concise sensitivity analysis of the quasi-linear viscoelastic model proposed by Fung. J Biomech Eng 105(1):92–95Rebouah M, Chagnon G (2014) Extension of classical viscoelastic models in large deformation to anisotropy and stress softening. Int J Non-Linear Mech 61:54–64Poon H, Ahmad MF (1998) A material point time integration procedure for anisotropic, thermo rheologically simple, viscoelastic solids. Comput Mech 21(3):236–242Drapaca CS, Sivaloganathan S, Tenti G (2007) Nonlinear constitutive laws in viscoelasticity. Math Mech Solids 12(5):475–501Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkHolzapfel GA (2000) Nonlinear solid mechanics. A continuum approach for engineering. Wiley, ChichesterPeña JA, Martínez MA, Peña E (2011) A formulation to model the nonlinear viscoelastic properties of the vascular tissue. Acta Mech 217(1–2):63–74Peña E, Peña JA, Doblaré M (2008) On modelling nonlinear viscoelastic effects in ligaments. J Biomech 41(12):2659–2666Holzapfel GA (1996) On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures. Int J Numer Methods Engrg 39(22):3903–3926Liefeith D, Kolling S (2007) An Anisotropic Material Model for Finite Rubber Viscoelasticity. LS-Dyna Anwenderforum, FrankenthalHaupt P (2002) Continuum mechanics and theory of materials, 2nd edn. Springer, BerlinBergström JS, Boyce MC (1998) Constitutive modeling of the large strain time-dependent behavior of elastomers. J Mech Phys Solids 46(5):931–954Le Tallec P, Rahier C, Kaiss A (1993) Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation. Comput Methods Appl Mech Eng 109:233–258Haupt P, Sedlan K (2001) Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling. Arch Appl Mech 71:89–109Lion A (1996) A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Contin Mech Thermodyn 8(3):153–169Lion A (1998) Thixotropic behaviour of rubber under dynamic loading histories: experiments and theory. J Mech Phys Solids 46(5):895–930Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Methods Appl Mech Eng 60(2):153–173Craiem D, Rojo FJ, Atienza JM, Armentano RL, Guinea GV (2008) Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries. Phys Med Biol 53:4543–4554Kaliske M, Rothert H (1997) Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Comput Mech 19(3):228–239Gasser TC, Forsell C (2011) The numerical implementation of invariant-based viscoelastic formulations at finite strains. An anisotropic model for the passive myocardium. Comput Methods Appl Mech Eng 200(49):3637–3645Reese S, Govindjee S (1998) A theory of finite viscoelasticity and numerical aspects. Int J Solids Struct 35(26):3455–3482Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12(2):93–99Sidoroff F (1974) Un modèle viscoélastique non linéaire avec configuration intermédiaire. J Mécanique 13(4):679–713Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36(1):1–6Bilby BA, Bullough R, Smith E (1955) Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc R Soc Lond Ser A 231(1185):263–273Herrmann LR, Peterson FE (1968) A numerical procedure for viscoelastic stress analysis. In: Seventh meeting of ICRPG mechanical behavior working group, Orlando, FL, CPIA Publication, vol 177, pp 60–69Taylor RL, Pister KS, Goudreau Gl et al (1970) Thermomechanical analysis of viscoelastic solids. Int J Numer Methods Eng 2(1):45–59Hartmann S (2002) Computation in finite-strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations. Comput Methods Appl Mech Eng 191(13–14):1439–1470Eidel B, Kuhn C (2011) Order reduction in computational inelasticity: why it happens and how to overcome it–The ODE-case of viscoelasticity. Int J Numer Methods Eng 87(11):1046–1073Haslach HW Jr (2005) Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomech Model Mechanobiol 3(3):172–189Pioletti DP, Rakotomanana LR, Benvenuti JF, Leyvraz PF (1998) Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J Biomech 31(8):753–757Merodio J, Goicolea JM (2007) On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics. Mech Res Commun 34(7):561–571Bonet J (2001) Large strain viscoelastic constitutive models. Int J Solids Struct 38(17):2953–2968Peric D, Dettmer W (2003) A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour. Eng Comput 20(5/6):768–787Nedjar B (2002) Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part I: continuum formulations. Comput Methods Appl Mech Eng 191(15):1541–1562Latorre M, Montáns FJ (2014) On the interpretation of the logarithmic strain tensor in an arbitrary system of representation. Int J Solids Struct 51(7):1507–1515Eterovic AL, Bathe KJ (1990) A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures. Int J Numer Methods Eng 30(6):1099–1114Simo JC (1992) Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput Methods Appl Mech Eng 99(1):61–112Caminero MA, Montáns FJ, Bathe KJ (2011) Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures. Comput Struct 89(11):826–843Montáns FJ, Benítez JM, Caminero MA (2012) A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution. Mech Res Commun 43:50–56Papadopoulos P, Lu J (2001) On the formulation and numerical solution of problems in anisotropic finite plasticity. Comput Meth Appl Mech Eng 190(37):4889–4910Miehe C, Apel N, Lambrecht M (2002) Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials. Comput Meth Appl Mech Eng 191(47):5383–5425Vogel F, Göktepe S, Steinmann P, Kuhl E (2014) Modeling and simulation of viscous electro-active polymers. Eur J Mech 48:112–128Holmes DW, Loughran JG (2010) Numerical aspects associated with the implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive theory in principal stretches. Int J Numer Methods Eng 83(3):366–402Holzapfel GA, Gasser TC, Stadler M (2002) A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. Eur J Mech 21(3):441–463Nguyen TD, Jones RE, Boyce BL (2007) Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites. Int J Solids Struct 44(25):8366–8389Nedjar B (2007) An anisotropic viscoelastic fibre-matrix model at finite strains: continuum formulation and computational aspects. Comput Methods Appl Mech Eng 196(9):1745–1756Latorre M, Montáns FJ (2013) Extension of the Sussman-Bathe spline-based hyperelastic model to incompressible transversely isotropic materials. Comput Struct 122:13–26Latorre M, Montáns FJ (2014) What-you-prescribe-is-what-you-get orthotropic hyperelasticity. Comput Mech 53(6):1279–1298Latorre M, Montáns FJ (2015) Material-symmetries congruency in transversely isotropic and orthotropic hyperelastic materials. Eur J Mech 53:99–106Miñano M, Montáns FJ (2015) A new approach to modeling isotropic damage for Mullins effect in hyperelastic materials. Int J Solids Struct 67–68:272–282Montáns FJ, Bathe KJ (2005) Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spin. Int J Numer Methods Eng 63(2):159–196Montáns FJ, Bathe KJ (2007) Towards a model for large strain anisotropic elasto-plasticity. Computational plasticity. Springer, New York, pp 13–36Bathe KJ (2014) Finite element procedures, 2nd edn. Klaus-Jurgen Bathe, BerlinWeber G, Anand L (1990) Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comput Methods Appl Mech Eng 79(2):173–202Hartmann S, Quint KJ, Arnold M (2008) On plastic incompressibility within time-adaptive finite elements combined with projection techniques. Comput Methods Appl Mech Eng 198:178–193Simo JC, Miehe C (1992) Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Comput Methods Appl Mech Eng 98(1):41–104Sansour C, Bocko J (2003) On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law. Int J Numer Methods Eng 58(14):2131–2160Bischoff JE, Arruda EM, Grosh K (2004) A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue. Biomech Model Mechanobiol 3(1):56–65Sussman T, Bathe KJ (2009) A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension-compression test data. Commun Numer Methods Eng 25:53–63Sussman T, Bathe KJ (1987) A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput Struct 26:357–409Ogden RW (1997) Nonlinear elastic deformations. Dover, New YorkKim DN, Montáns FJ, Bathe KJ (2009) Insight into a model for large strain anisotropic elasto-plasticity. Comput Mech 44(5):651–66